We know if we send a spaceship accelerating away from the Earth its clocks will run more slowly than clocks left on Earth.
However, the earth itself is in a state of constant acceleration. We rotate on our axis, we orbit the sun, the sun orbits the galaxy and the galaxy itself is moving.
So, shouldn’t we be able to maneuver a spaceship in a fashion where the clocks on the spaceship run faster than those on earth (thinking accelerate in some direction, turn off the engines and coast then compare your clock to those on earth…rinse and repeat till you achieve the biggest difference between the two clocks). Surely we could achieve motion where the earth is moving more quickly than the spaceship.
At that point could we not say that, as near as is possible, the spaceship indeed is the thing not moving and everything else moves relative to the spaceship?
I have no doubt that is in error…guess I am asking why it would not work.
Twin Paradox.
Also I think you’ve confused acceleration and velocity in your OP.
Perhaps.
Tweak my premise to suppose the spaceship is under acceleration but keeps maneuvering and adjusting so its clocks run more quickly than ours on earth.
You are actually right in what you’re saying. What I think you might be confused about is the difference between an accelerating reference frame and a reference frame that’s moving at a constant speed. You can always tell absolute acceleration (leaving aside gravity for now): there’s nothing relative about acceleration. But speed is always relative.
So, for instance if the only things in the universe were three spaceships. Two of them are moving in opposite directions at a constant speed, while the third is accelerating in another direction. The third one is accelerating from anyone’s point of view, but nobody can say whether the first one is stationary while the second is moving away, or the second is stationary while the first moves away.
I presume a clock on Pluto runs faster than one on earth (that is the earth has a greater orbital velocity…being circular motion I believe it means we are under constant acceleration).
So right there we have found a way to move where we see earth’s clocks running more slowly due to acceleration than somewhere else in the solar system.
So why can we not keep tweaking the parameters of our motion to make the biggest difference thus saying object_x is as close to relative rest compared to earth as is possible?
Somebody brought this up recently, but nobody addressed it. Couldn’t an observer floating in deep space be said to be at complete rest if he measures the Doppler shift of the CMB in every direction and detects no variance?
We can do that. The motion that meets the parameters is free-fall.
You get time dilation even when there’s just a difference in speeds, no acceleration required.
If you’re in a rocket ship moving away from the Earth, then in your frame of reference the Earth’s clocks are running slow and in the Earth’s frame of reference your clock is running slow. Why isn’t this a paradox? Well, because in order to bring your clock and an Earth clock back together in order to compare them, you have to switch to a new frame of reference (corresponding to motion back towards the Earth). In that frame of reference, the Earth’s clocks are running slow but the initial outgoing rocket’s clock ran even slower. Thus the math is able to work out so that by the time you get back to Earth you and the observers on Earth all agree on what the difference between the Earth clock and the rocket clock should be.
The stars aren’t fixed in relationship to each other. They’ll all have Doppler shifts and in various directions.
Even if you move out between galaxies, you’ll notice the galaxies themselves moving in all directions and all will have different Doppler shifts.
The only thing you can tell if you are experiencing some form of change in acceleration or not. If you don’t experience any change in acceleration, you can assume you are at rest, but this is also true if you fall down an elevator shaft.
Yes, there is a rest frame relative to the CMB. When various telescopes measure the CMB, they have to subtract off the effect of the doppler shift due to our own motion relative to it. I don’t know if I’d call that frame “complete rest”, but presumably its the rest frame of the early universe.
I didn’t see the question about the CMB before. At any given location, there’s a reference frame where the CMB shows no net Doppler shift, but it’s a different reference frame at every location. So if I put myself at rest “relative to the CMB”, and there’s someone else a few billion lightyears away at rest relative to me, then he’s not at rest “relative to the CMB”. This is possible because the CMB he’s seeing is different than the one I’m seeing.
I have an unrelated question which has been pestering me a while, and now seems as good a time as any to bring it up. If an observer were traveling at the speed at which the CMB would be shifted into the visible light range, what would he see? Would the universe suddenly ‘light up’?
Ahead of him, at least, yes, but it’d be redshifted even further from visibility behind him.